In terms of the subleading soft graviton operator - again denoted by \(S_{ab}(\vec{w})\)  - Cachazo-Strominger subleading soft graviton theorem [1]} can be written as,
\({\begin{array}{c}{\lbrace y_i,\vec{x}_i\rbrace ,out} S_{ab}(\vec{w}) {\lbrace y_j,\vec{x}_j\rbrace ,in} \\ = -i \sum _k \eta _k \frac{\epsilon _{ab}^{\mu \nu }(\vec{w})p^k_{\mu }q^{\rho }}{p^k\cdot q} J^k_{\rho \nu } {\lbrace y_i,\vec{x}_i\rbrace ,out}{\lbrace y_j,\vec{x}_j\rbrace ,in}\end{array}}\) 
